> ## Documentation Index
> Fetch the complete documentation index at: https://docs.chicago.global/llms.txt
> Use this file to discover all available pages before exploring further.

# Information Coefficient

> Understanding the Information Coefficient - measuring forecasting skill

The Information Coefficient (IC) measures how good you are at predicting which stocks will outperform. It's the correlation between your predictions and actual outcomes - the purest measure of investment skill.

## Beginner

### What It Means

IC answers: "When I predict a stock will do well, how often is that prediction correct?" It's measured as a correlation, ranging from -1 to +1.

### Portfolio Example

At the start of each quarter, you predict expected returns for 100 stocks. At quarter end, you compare predictions to actual returns.

| IC Value | Interpretation                          |
| -------- | --------------------------------------- |
| 0.00     | No predictive ability (random guessing) |
| 0.03     | Weak but positive skill                 |
| 0.05     | Typical skilled manager                 |
| 0.10     | Strong skill (rare)                     |

### Why It Matters

IC directly measures forecasting skill - the core of active management value. If you can't predict which stocks will outperform, you can't add value. IC tells you if your predictions have any merit.

***

## Advanced

### Mathematical Definition

```
IC = Correlation(Forecast Returns, Realized Returns)

IC = Cov(f, r) / (σf × σr)

Where:
- f = Forecasted returns
- r = Realized returns
- Range: -1.0 to +1.0
```

### Realistic IC Values

Most investors overestimate achievable IC:

| Manager Type   | Typical IC     |
| -------------- | -------------- |
| Bottom Decile  | -0.02 to +0.01 |
| Median Manager | 0.02 - 0.04    |
| Top Quartile   | 0.05 - 0.08    |
| Top Decile     | 0.08 - 0.12    |

<Warning>
  An IC of 0.10 is exceptional. Claims of IC above 0.15 should be viewed with extreme skepticism.
</Warning>

### The Fundamental Law of Active Management

IC connects to expected performance through:

```
E(IR) = IC × √BR

Where:
- IR = Information Ratio
- IC = Information Coefficient
- BR = Breadth (independent bets per year)
```

**Example:**

* IC = 0.05, BR = 100 independent bets
* E(IR) = 0.05 × √100 = 0.05 × 10 = 0.50

### Why Small IC Matters

Even tiny IC creates value with enough breadth:

| IC   | Breadth | Expected IR |
| ---- | ------- | ----------- |
| 0.02 | 100     | 0.20        |
| 0.05 | 100     | 0.50        |
| 0.05 | 400     | 1.00        |
| 0.10 | 100     | 1.00        |

<Note>
  The law shows two paths to high IR: better skill (higher IC) or more independent bets (higher breadth). Most quant strategies focus on breadth since IC is hard to improve.
</Note>

### IC Stability

IC is not constant:

| Factor                | Effect on IC                             |
| --------------------- | ---------------------------------------- |
| **Market Volatility** | Higher dispersion = higher achievable IC |
| **Regime Changes**    | IC varies across bull/bear markets       |
| **Strategy Crowding** | More users = lower IC                    |
| **Information Decay** | Signals lose power over time             |

### Measuring IC

| Approach             | Description                                        |
| -------------------- | -------------------------------------------------- |
| **Cross-Sectional**  | Rank correlation each period across all stocks     |
| **Time-Series**      | Track individual stock forecast accuracy over time |
| **Quintile Spreads** | Top quintile return minus bottom quintile          |

### Data Requirements

| Requirement     | Details                                 |
| --------------- | --------------------------------------- |
| Observations    | 100+ independent forecasts minimum      |
| Preferred       | 500+ forecasts for stable IC estimate   |
| Time Coverage   | Multiple periods to confirm consistency |
| Cross-Sectional | 50-100 stocks per period typical        |

### Limitations

| Limitation              | Description                                    |
| ----------------------- | ---------------------------------------------- |
| **Hard to Measure**     | Requires detailed forecast data                |
| **Time-Varying**        | IC changes across market conditions            |
| **Implementation Gap**  | Forecast IC differs from realized portfolio IC |
| **Correlation Effects** | High correlations reduce effective breadth     |

### IC vs. Hit Ratio

| Metric        | Measures                       | Considers Magnitude? |
| ------------- | ------------------------------ | -------------------- |
| **Hit Ratio** | Frequency of correct direction | No                   |
| **IC**        | Correlation with outcomes      | Yes                  |

IC is more comprehensive because it accounts for both direction and magnitude of predictions.

### Related Terms

<CardGroup cols={3}>
  <Card title="Information Ratio" href="/glossary/information-ratio">
    IC helps determine IR
  </Card>

  <Card title="Hit Ratio" href="/glossary/hit-ratio">
    Related but simpler measure
  </Card>

  <Card title="Alpha" href="/glossary/alpha">
    What IC enables
  </Card>
</CardGroup>